Problem: Solve for $x$ and $y$ using elimination. $\begin{align*}4x-6y &= -7 \\ 4x-3y &= 2\end{align*}$
Answer: We can eliminate $x$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-1$ and the bottom equation by $1$ $\begin{align*}-4x+6y &= 7\\ 4x-3y &= 2\end{align*}$ Add the top and bottom equations. $3y = 9$ Divide both sides by $3$ and reduce as necessary. $y = 3$ Substitute $3$ for $y$ in the top equation. $4x-6( 3) = -7$ $4x-18 = -7$ $4x = 11$ $x = \dfrac{11}{4}$ The solution is $\enspace x = \dfrac{11}{4}, \enspace y = 3$.